Demodulation of data streams transmitted synchronously by several users over a Gaussian multiple access channel is considered. Each user modulates a different signal from a linearly independent signal set. The asymptotic efficiency criterion is used to evaluate the perfomance of different detection rules. The two currently most important detectors are presented and compared: the optimum multiuser detector whose complexity is exponential in the number of users and the single user detector whose performance degrades very rapidly as the multiuser interference energy increases. In contrast, a memoryless linear transformation on the matched filter outputs of the receiver is proposed, which is shown to guarantee a high lower bound on the asymptotic efficiency, which is independent of signal energies, while the time-complexity per bit is linear in the number of users. An algorithm which finds the best linear transformation is given, along with sufficient conditions on the signal energies and crosscorrelations to ensure optimum asymptotic efficiency of the proposed detector.